A math learning center is a place in the classroom where students either refine a skill that has already been learned, or extend upon that skill. A math station is designed to assist students who might be struggling with certain concepts, and helps the teacher address those issues individually.
Both centers and stations are located throughout the classroom, however, the difference lies in the actual student involvement. Centers use a round-robin approach, which allows students to visit various centers either individually or in groups, while students in stations remain at the station in order to receive more direct help on a particular topic from their teacher.
In a center, the teacher is more of an observer, assisting students when they need help, since they have already mastered the concepts. In a station, the teacher is more directly involved and takes time in each station to assist the students and reinforce concepts.
Math centers can implement the use of manipulatives in order to reinforce concepts, yet an assignment can be given. However, if you wish for the students to rotate, the assignment must be able to be completed in the time allowed. On the other hand, since stations do not require the students to move from one station to another, an assignment can be given; this allows the teacher to lead the students through it and answer any questions they may have.